"Julian, there are quite a bit of typos on your site."

Maybe you meant:

"Julian, there are quite a few typos on your site."

The phrase "quite a bit of" refers to something you measure, not something you count. And it would never be worded "there are quite a bit of..."

So you might say:

"There are quite a few eggs in that basket."

"There is quite a bit of snow on that mountain."

(edit with one more thought...)

One good way to help keep this straight is to remove the word "quite":

"There are a few eggs in that basket."

"There is a bit of snow on that mountain."